A default hierarchy is set of rules containing one
or more exceptions to one or more default rules e.g. all dogs
are friendly, except my neighbour’s. Default hierarchies were
the subject of considerable interest in early Learning Classifier
Systems research, but they were abandoned due to the
considerable difficulty of solving the credit assignment problems they
involve. The most popular Learning Classifier System, XCS, and
its derivatives do not support default hierarchies because in XCS
each rule must be accurate, whereas in a default hierarchy an
overgeneral rule may be overridden by a correct rule. In this
work we enable XCS to evolve minimal default hierarchies by
allowing two conditions in one rule, but evaluating only the
accuracy and fitness of the whole as a whole. This simple step
avoids the credit assignment issues faced by earlier systems.
We call this XCS-DH. Preliminary evaluation of XCS-DH on
a number of Boolean functions indicates a strong tendency
to exploit the increased expressiveness of its rules. On some
functions we observe slower learning and a larger population size,
which we attribute to the increased rule expressiveness, which
increases the search space. However, we also observe that in a
problem that is particularly suitable for XCS-DH representation,
and that is sufficient difficult for XCS, XCS-DH’s learning rate is
faster than XCS’s. We take this as confirmation of the potential
of learning default hierarchies with XCS-DH.